On some applications of fuzzy points

Maximilian Ganster; D. N. Georgiou; S. Jafari; S. P. Moshokoa

doi:10.4995/agt.2005.1951

Authors

Maximilian Ganster Graz University of Technology
D. N. Georgiou University of Patras
S. Jafari Roskilde University
S. P. Moshokoa University of South Africa

DOI:

https://doi.org/10.4995/agt.2005.1951

Keywords:

Fuzzy Topology, Fuzzy points, Fuzzy convergence, Fuzzy separation axioms, Fuzzy preopen sets

Abstract

The notion of preopen sets play a very important role in General Topology and Fuzzy Topology. Preopen sets are also called nearly open and locally dense. The purpose of this paper is to give some applications of fuzzy points in fuzzy topological spaces. Moreover, in section 2 we offer some properties of fuzzy preclosed sets through the contribution of fuzzy points and we introduce new separation axioms in fuzzy topological spaces. Also using the notions of weak and strong fuzzy points, we investigate some properties related to the preclosure of such points, and also their impact on separation axioms. In section 3, using the notion of fuzzy points, we introduce and study the notions of fuzzy pre-upper limit, fuzzy pre-lower limit and fuzzy pre-limit. Finally in section 4, we introduce the fuzzy pre-continuous convergence on the set of fuzzy pre-continuous functions and give a characterization of the fuzzy pre-continuous convergence through the assistance of fuzzy pre-upper limit.

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Author Biographies

Maximilian Ganster, Graz University of Technology

Department of Mathematics

D. N. Georgiou, University of Patras

Department of Mathematics

S. Jafari, Roskilde University

Department of Mathematics and Physics

S. P. Moshokoa, University of South Africa

Department of Mathematics, Applied Mathematics and Astronomy

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